The complex incidence matrix of a signed graph containing ambivalent ties.
Details
This function is slightly different than as_incidence_matrix since it is defined for bipartite graphs. The incidence matrix here is defined as a \(S \in C^{n,m}\), where n is the number of vertices and m the number of edges. Edges (i,j) are oriented such that i<j and entries are defined as $$S_{i(i,j)}=\sqrt{A_{ij}}$$ $$S_{j(i,j)}=-\sqrt{A_{ji}} if (i,j) is an ambivalent tie$$ $$S_{j(i,j)}=-A_{ji}\sqrt{A_{ji}} else$$